Online shoe and apparel shop Zappos.com is advising over 24 million customers to change their passwords following a data breach, but its website is currently inaccessible to people outside the U.S.

Zappos employees received an email from CEO Tony Hsieh on Sunday, alerting them about a security breach that involved the online shop's customer database.

"We were recently the victim of a cyber attack by a criminal who gained access to parts of our internal network and systems through one of our servers in Kentucky. We are cooperating with law enforcement to undergo an exhaustive investigation," Hsieh said in the email.

Even though he assured everyone that no credit card details had been compromised, Hsieh revealed that the attacker had accessed customer records including names; email, billing and shipping addresses; phone numbers, and the last four digits of their credit card numbers.

The hacker also gained access to password hashes for the accounts registered on the website, prompting the company to reset everyone's access codes. Zappos is currently in the process of emailing its 24 million customers in order to notify them about the security breach and advise them to change their passwords.

The company also took the decision to shut off its phones, because the expected phone traffic generated by customers calling in would almost certainly exceed what its system can handle. Customer support is currently being provided through email and Twitter.

"Please create a new password by visiting Zappos.com and clicking on the 'Create a New Password' link in the upper right corner of the web site and follow the steps from there," the company said in its email to customers.

However, at the moment, non-US residents cannot access most of Zappos' website, leaving them unable to follow these instructions. "We are currently undergoing some system maintenance that has limited our international customers in accessing our website," the company said via Twitter.

Zappos advised its customers to change their login details on any other websites where they used the same password, to prevent hackers trying to access those accounts using the data they obtained during this breach.

It's not clear whether affected customers will be offered identity theft protection services or not. Zappos, which is a subsidiary of Amazon, did not immediately return a request for comment regarding this possibility.